Association of infinitely divisible random vectors
type: Item
instance of: scholarly article
title: Association of infinitely divisible random vectors
zbMATH Open document ID: 0817.60009
DOI: 10.1016/0304-4149(93)00017-A
author: Gennady Samorodnitsky
published in: Stochastic Processes and their Applications
publication date: 1995-07-17T00:00:00Z
review text: The (components of a) random vector \(X\) in \(\mathbb{R}^ d\), \(d \geq 2\), are called associated if \(\text{cov} (f(X)\), \(g(X)) \geq 0\) for any two nondecreasing, real functions \(f\) and \(g\). It is known that for an infinitely divisible (inf div) random vector to be associated it is sufficient that its Lévy measure to be concentrated on the two orthants \(\mathbb{R}^ d_ +\) and \(\mathbb{R}^ d_ -\). The author shows that this condition, which I call C here, is not necessary, by constructing an example of an associated inf div random vector in \(\mathbb{R}^ 2\) that does not satisfy condition C. Further two examples are given: one showing that C is equivalent to a stronger notion than association, another presenting a class of inf div random vectors for which C is equivalent to association.
Mathematics Subject Classification ID: 60E07
Mathematics Subject Classification ID: 62H20
zbMATH DE Number: 735471
zbMATH Keywords: dependence
zbMATH Keywords: infinitely divisible
zbMATH Keywords: Lévy measure
zbMATH Keywords: association
reviewed by: Fred W. Steutel
MaRDI profile type: Publication
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full work available at URL: 0304-4149(93)00017-a
OpenAlex ID: W1987931068
description: scientific article; zbMATH DE number 735471